Missing Inferred Type in Tooltip when using Visible Type Applications

### Your environment

Which OS do you use?
ArchLinux

Which version of GHC do you use and how did you install it?
9.6.4 from ghcup

How is your project built (alternative: link to the project)?
cabal

Which LSP client (editor/plugin) do you use?
Code - OSS + vscode-haskell

Which version of HLS do you use and how did you install it?
2.6.0.0 from ghcup

Have you configured HLS in any way (especially: a `hie.yaml` file)?
```
"haskell.manageHLS": "PATH",
"haskell.plugin.importLens.codeActionsOn": false,
"haskell.plugin.class.codeActionsOn": false,
"haskell.plugin.semanticTokens.globalOn": true,
```

### Steps to reproduce

Hovering over `print` in this example:
```hs
main = (print :: Int -> IO ()) 0
```

Hovering over `print` in this example:
```hs
main = print @Int 0
```

### Expected behaviour

The inferred type for `print` is shown in the tooltip in both examples.

### Actual behaviour

The inferred type for `print` is only shown with type annotations via `::`, but not with visible type applications via `@`. The inferred type is shown correctly without any type annotations (together with a warning about defaulting the type variable to `Integer`).

### Debug information

I could not find anything relevant in the HLS output log either when typing the expression or when hovering to produce the tooltip.

Reproduce the tooltip behavior in HLS with the two examples, comparing the `::` annotation and `@Int` visible type application forms. Trace the hover handling for the `print` expression and verify that the inferred type appears for both forms while preserving the existing behavior for unannotated code.

Written by the indexing model from the issue text.